Improving sample efficiency of high dimensional Bayesian optimization with MCMC

TL;DR

This paper introduces a novel MCMC-based approach to improve the sample efficiency of high-dimensional Bayesian optimization, addressing computational challenges and outperforming existing methods in complex benchmarks.

Contribution

The paper proposes a new MCMC sampling method within Gaussian process Bayesian optimization, with theoretical convergence guarantees and superior empirical performance.

Findings

Outperforms state-of-the-art methods in high-dimensional benchmarks

Provides theoretical convergence guarantees for the proposed MCMC approach

Enhances sample efficiency in high-dimensional Bayesian optimization

Abstract

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking Gaussian process posteriors and need to partition the optimization problem into small regions to ensure exploration or assume an underlying low-dimensional structure. With the idea of transiting the candidate points towards more promising positions, we propose a new method based on Markov Chain Monte Carlo to efficiently sample from an approximated posterior. We provide theoretical guarantees of its convergence in the Gaussian process Thompson sampling setting. We also show experimentally that both the Metropolis-Hastings and the Langevin Dynamics version of our algorithm outperform state-of-the-art methods in high-dimensional sequential optimization and reinforcement learning benchmarks.